In the engine of German OS No. 1,916,098 liquid is conducted through a heat exchanger connected to the exhaust system as long as the liquid is below the operating temperature, so that the liquid can absorb heat from the exhaust gases and thereby the warm-up time of the engine is substantially reduced. With rising temperature the liquid is conducted in increasing quantities through the radiator by means of a thermostat mounted in the coolant circuit, so that the operating temperature which is required for the engine is maintained. However, with this arrangement there remains in the heat exchanger a quantity of liquid which now becomes excessively heated and, as a consequence of the connections to the liquid circuit which are open to a greater or lesser extent according to the operating condition, this can have an adverse effect on the circuit and can lead to substantial additional load on the radiator.